Coding theory

Coding theory

Détails bibliographiques
Auteur principal : Lint Jacobus Hendricus van (Auteur)
Format : Livre
Langue : anglais
Titre complet : Coding theory / Jacobus H. Van Lint, ...
Publié : Berlin, Heidelberg, New York : Springer , cop. 1971
Description matérielle : 1 vol. (VI-136 p.)
Collection : Lecture notes in mathematics ; 201
Sujets :
Codage
  • Chapter I. Introduction
  • 1.1 Channels, noise, redundancy
  • 1.2 An introductory example
  • 1.3 Some definitions in onformation theory
  • 1.4 Shannon's fundamental theorem
  • 1.5 Problems
  • Chaper II. Linear codes
  • 2.1 General theory
  • 2.2 Hamming codes
  • 2.3 Reed-Muller codes
  • 2.4 Threshold decoding
  • 2.5 Direct-product codes
  • 2.6 Problems
  • Chapter III. Cyclic codes
  • 3.1 Introduction
  • 3.2 The zeros of a cyclic code
  • 3.3 Idempotents
  • 3.4 Some other representations of cyclic codes
  • 3.5 Problems
  • Chapter IV. Important cyclic codes
  • 4.1 BCH codes
  • 4.2 Reed-Solomon codes
  • 4.3 Generalized Reed-Muller codes
  • 4.4 Quadratic residue codes
  • 4.5 Problems
  • Chapter V. Perfect coes
  • 5.1 Perfect single-error-correcting codes
  • 5.2 The sphere-packing condition
  • 5.3 The Golay codes
  • 5.4 Lloyd's theorem
  • 5.5 Nonexistence theorems
  • Chapter VI. Weight enumeration
  • 6.1 The Macwilliams equations
  • 6.2 Weight enumeration of Reed-Muller codes
  • 6.3 The Carlitz-Uchiyama bound